Jeans massradius relation of selfgravitating BoseEinstein condensates and typical parameters of the dark matter particle
Abstract
We study the Jeans massradius relation of BoseEinstein condensate dark matter in Newtonian gravity. We show at a general level that it is similar to the core massradius relation of BoseEinstein condensate dark matter halos [P. H. Chavanis, Phys. Rev. D 84, 043531 (2011), 10.1103/PhysRevD.84.043531]. Bosons with a repulsive selfinteraction generically evolve from the ThomasFermi regime to the noninteracting regime as the Universe expands. In the ThomasFermi regime, the Jeans radius remains approximately constant while the Jeans mass decreases. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. Bosons with an attractive selfinteraction generically evolve from the nongravitational regime to the noninteracting regime as the Universe expands. In the nongravitational regime, the Jeans radius and the Jeans mass increase. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. The transition occurs at a maximum Jeans mass which is similar to the maximum core mass of BoseEinstein condensate dark matter halos with an attractive selfinteraction. We use the core massradius relation of dark matter halos and the observational evidence of a "minimum halo" (with typical radius R ∼1 kpc and typical mass M ∼10^{8} M_{⊙}) to constrain the mass m and the scattering length a_{s} of the dark matter particle. For noninteracting bosons, m is of the order of 2.92 ×10^{22} eV /c^{2}. The mass of bosons with an attractive selfinteraction can be only slightly smaller (2.19 ×10^{22} eV /c^{2}<m <2.92 ×10^{22} eV /c^{2} and 1.11 ×10^{62} fm ≤a_{s}≤0 ); otherwise, the minimum halo would be unstable. Constraints from particle physics and cosmology imply m =2.92 ×10^{22} eV /c^{2} and a_{s}=3.18 ×10^{68} fm for ultralight axions, and it is then found that attractive selfinteractions can be neglected in both the linear and the nonlinear regimes of structure formation. The mass of bosons with a repulsive selfinteraction can be larger by 18 orders of magnitude (2.92 ×10^{22} eV /c^{2}<m <1.10 ×10^{3} eV /c^{2} and 0 ≤a_{s}≤4.41 ×10^{6} fm ). The maximum allowed mass (m =1.10 ×10^{3} eV /c^{2} and a_{s}=4.41 ×10^{6} fm ) is determined by the Bullet Cluster constraint while the transition between the noninteracting limit and the ThomasFermi limit corresponds to m =2.92 ×10^{22} eV /c^{2} and a_{s}=8.13 ×10^{62} fm . For each of these models, we calculate the Jeans length and the Jeans mass at the epoch of radiationmatter equality and at the present epoch.
 Publication:

Physical Review D
 Pub Date:
 June 2021
 DOI:
 10.1103/PhysRevD.103.123551
 arXiv:
 arXiv:2011.01038
 Bibcode:
 2021PhRvD.103l3551C
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Astrophysics of Galaxies
 EPrint:
 Phys. Rev. D 103, 123551 (2021)